Alternate Interior Angles Theorem and Alternate Exterior Angles Theorem , 4

Ⓐⓛⓣⓔⓡⓝⓐⓣⓔ Ⓘⓝⓣⓔⓡⓘⓞⓡ Ⓐⓝⓖⓛⓔⓢ Ⓣⓗⓔⓞⓡⓔⓜ ⓐⓝⓓ Ⓐⓛⓣⓔⓡⓝⓐⓣⓔ Ⓔⓧⓣⓔⓡⓘⓞⓡ Ⓐⓝⓖⓛⓔⓢ ⓉⓗⓔⓞⓡⓔⓜBy: Amanda Koch, Andie Drummond, Caroline Fiss and Sara Schwartz, Period 4








Proof.
Since k || l, by the Corresponding Angles Postulate,

angle

1

is congruent to

angle

5.
Therefore, by the definition of congruent angles,
m

angle

1 = m

angle

5.
Since

angle

1 and

angle

2 form a linear pair, they aresupplementary, so
m

angle

1 + m

angle

2 = 180°.
Also,

angle

5 and

angle

8 are supplementary, so
m

angle

5 + m

angle

8 = 180°.
Substituting m

angle

1 for m

angle

5, we get
m

angle

1 + m

angle

8 = 180°.
Subtracting m

angle

1 from both sides, we have
m

angle

8 = 180° − m

angle

1 = m

angle

2.
Therefore,

angle

2

is congruent to

angle

8.
You can prove that

angle

3

is congruent to

angle

5 using the same method.



If you are unable to see the picture, go to http://www.mathwords.com/a/alternate_interior_angles.htm.
The two horizontal lines are parallel, which are the alternate interior angles? Which are alternate exterior angles?

Answer to 3 shown as 2.
The value of x is 54. X is 54 because the measure of angle 8 is 112. The measure of angle 8 is 112 because angle 3 is congruent to angle 2 because of the vertical angle congruence theorem, and angle 2 is congruent to angle 7 because of the alternate interior angle's theorem, and the measure of angle 8 + the measure of angle 7 =180 degrees because they are a linear pair. Then you solve for x, (2x+4)=112. Because you know that the measure of angle 8 = 2x +4.
Answer to 5, Alternate exteriors angles: angle 3 and angle 6, angle 4 and angle 5. Alternate Exterior: angle 2 and angle 7, angle 1 and angle 8. You can also solve this problem using the alternate exterior angles theorem, because angle 1 and angle 8 are alternate exterior angles, and angle 1 is 112 because it is supplementary to angle 3, then solve using the same equation, 2x+4=112, x=54.
Very Helpful Websites!!http://www.mathwarehouse.com/geometry/angle/transveral-and-angles.php
http://hotmath.com/hotmath_help/topics/alternate-interior-angles-theorem.html
http://www.mathsisfun.com/geometry/alternate-interior-angles.html

Websites we used to make this wiki:
http://www.classzone.com/cz/books/geometry_2007_na/secured/resources/applications/ebook/index.jsp